1. On line graphs with maximum energy.
- Author
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Lenes, Eber, Mallea-Zepeda, Exequiel, Robbiano, María, and Rodríguez Z., Jonnathan
- Subjects
- *
GEOMETRIC vertices , *GRAPHIC methods , *EIGENVALUES , *MATHEMATICAL bounds , *MATRICES (Mathematics) - Abstract
For an undirected simple graph G , the line graph L ( G ) is the graph whose vertex set is in one-to-one correspondence with the edge set of G where two vertices are adjacent if their corresponding edges in G have a common vertex. The energy E ( G ) is the sum of the absolute values of the eigenvalues of G . The vertex connectivity κ ( G ) is referred as the minimum number of vertices whose deletion disconnects G . The positive inertia ν + ( G ) corresponds to the number of positive eigenvalues of G . Finally, the matching number β ( G ) is the maximum number of independent edges of G . In this paper, we derive a sharp upper bound for the energy of the line graph of a graph G on n vertices having a vertex connectivity less than or equal to k . In addition, we obtain upper bounds on E ( G ) in terms of the edge connectivity, the inertia and the matching number of G . Moreover, a new family of hyperenergetic graphs is obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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